Beating the sign problem in finite density lattice QCD

Abstract

We report our recent project to study the QCD phase diagram by the canonical approach (CA), which is expected to solve the sign problem. First we briefly describe the sign problem and several approaches to fight against it. Then we argue that the CA may be a break-through if we combine it with the multiple precision calculation. We study the method using the hopping parameter expansion (HPE), in order to investigate how the CA works. We show explicitly how we calculate the winding number in HPE and obtain the fugacity expansion whose coefficients are the canonical partition functions. Finally we discuss dark sides of the current CA, which should be beaten for the method to become a real tool of QCD phase explorers.

Sign problem in finite density lattice QCD

“…(3) Winding number expansion [12,13] In this letter, we employ method (3), in which the fermion determinant det ∆ is expanded as a series of the hopping parameter κ, and the diagrams are classified and packed with respect to the fugacity power:…”

Study of high density phase transition in lattice QCD with canonical approach

“…A part of the results has been reported in Ref. [14,15]. For a detailed explanation of the numerical method to calculate the canonical partition function Z C (n, T,V ) please see Ref.…”